Explore a 47-minute lecture on "Homological Percolation in a Torus" presented by Paul Duncan from The Hebrew University of Jerusalem at IPAM's Statistical Mechanics Beyond 2D Workshop. Delve into the concept of percolation transitions in higher dimensional cell complexes and discover a novel approach to defining percolation on compact manifolds using algebraic topology. Learn about the emergence of global loops and their higher dimensional analogues as markers for this homological percolation. Examine proof of a phase transition for homological percolation in all dimensions on a large torus, considering both independent percolation and a generalization of the random-cluster model. Gain insights from this joint work with Benjamin Schweinhart and Matthew Kahle, expanding your understanding of statistical mechanics beyond traditional two-dimensional models.